Parents of very overweight children - those above the 95 centile - were extremely unlikely to recognise the problem, with just one in 100 parents classifying them correctly.

Only parents of those with the very highest body mass indexes - in the top 0.3 per cent of weights - accurately classes their children's weights.

According to official guidelines, children are classified as overweight at the 85th centile and very overweight (or obese) at the 95th centile.

More than a third of kids in England are now classed as overweight or obese by the time they leave primary school.

Researchers said parents may have been blinded to their children's unhealthy weight because the norm has risen so much.

They raised concerns that parents who could not identify the problem would be less likely to be able to help their children eat more healthily.

The study questioned the parents of 2,976 children in London, Birmingham, Somerset and Essex.

Senior author Dr Sanjay Kinra, reader in clinical epidemiology at the London School of Hygiene & Tropical Medicine, said: "If parents are unable to accurately classify their own child's weight, they may not be willing or motivated to enact the changes to the child's environment that promote healthy weight maintenance."